Direct method of calculating nonstationary temperature fields in bodies of basic geometric shapes

The authors propose a simultaneous solution to one-parameter heat-conduction problems for multilayer structures of basic (simple) geometric shapes with the direct (classical) method of investigation of the process of heat transfer. The presence of internal heat sources in the layers of such a structure and of ideal thermal contact between the layers with boundary conditions of the third kind on their bounding surfaces is assumed. In this connection, the authors solve the heat-conduction equation with a parameter having the meaning of the shape factor of a body. The reduction method, the concept of quasi derivatives, the present-day theory of systems of linear differential equations, the method of separation of variables, and a modifi ed Fourier method of eigenfunctions are used as a basis for the solution scheme. A model example of numerical calculation of the temperature fi eld in fi ve-layer structures (rectangular wall, a hollow cylinder, and a hollow sphere) is given.
The authors propose a simultaneous solution to one-parameter heat-conduction problems for multilayer structures of basic (simple) geometric shapes with the direct (classical) method of investigation of the process of heat transfer. The presence of internal heat sources in the layers of such a structure and of ideal thermal contact between the layers with boundary conditions of the third kind on their bounding surfaces is assumed. In this connection, the authors solve the heat-conduction equation with a parameter having the meaning of the shape factor of a body. The reduction method, the concept of quasi derivatives, the present-day theory of systems of linear differential equations, the method of separation of variables, and a modifi ed Fourier method of eigenfunctions are used as a basis for the solution scheme. A model example of numerical calculation of the temperature fi eld in fi ve-layer structures (rectangular wall, a hollow cylinder, and a hollow sphere) is given.
Author:  R. M. Tatsii, M. F. Stasyuk, O. Yu. Pazen
Keywords:  reduction, quasi derivative, Cauchy matrix, method of eigenfunctions, shape factor of a body
Page:  298-310